Bridging the Gap from Continuum Mechanics to Molecular Dynamics for Nanoscale Systems
thesisposted on 2015-07-21, 00:00 authored by Qilu He
Bending nanowires and nanoplates are widely used as flexible beams in Nano-Electro-Mechanical Systems for force and mass sensors. Usually, the vertical deflection and resonant frequencies of the nanowires and plates are the most crucial parameters in these systems. Deriving the mechanical theories specifically applicable to nanoscale materials and enhancing the accuracy of the mechanics of these nanoscale structures is still a bottle neck in designing nanotechnology. Typically, there are two different ways to accomplish the mechanical modeling for nanoscale materials, such as modeling with continuum mechanics by adding size effects and modeling from atomic scale theory. However, both of these methods have some fundamental issues or limitations and cannot be directly applied to accurately achieve accurate mechanical modeling for nanoscale materials. The hypothesis of this dissertation is that the Euler-Bernoulli or Timoshenko beam theory with surface effects, Eringen’s nonlocal elasticity and the corresponding nonlocal beam theories, and molecular dynamics simulations results should all be consistent for nanoscale structures with critical dimensions of 1-100nm. First, a more general solution of continuum beam theories with surface effect has been obtained and developed to investigate the surface effect on bending nanowires with the “core-shell” approach. Timoshenko beam theory with surface effects has been applied with consideration of shear effect and rotational inertia effect. Consequently, the limitation of aspect ratio of Euler-Bernoulli beam theory was eliminated. Second, the solutions of the resonant frequencies with surface stress effect and nonlocal effect have been compared. A bridging theory by incorporating surface properties with the nonlocal elasticity theory parameter e0 has been developed to bridge the classical beam theories with nonlocal beam theory at the nanoscale. Finally, molecular dynamics simulations have also been introduced to verify the above conclusions from the theoretical relation between the surface stress and nonlocal parameter. The molecular dynamics simulations found the same trends as the theoretical modeling predicts. An imaginary e0 was also found by calibrating e0 with the resonant frequencies obtained from the molecular dynamics simulations. The future work has been discussed at the end of the dissertation.